Yup (this "yup" was in reference to Sidroe's post... the rest is just bored blathering). To find the relative minor of a Major key go forward six steps in the scale or 3 steps back from the root.
When we talk about modes and relative Majors/minors all that is happening is we are taking the same 7 notes and changing the start/end point of the scale. There are twelve keys so that means we have twelve such patterns using the Natural Major pattern and each of those twelve has a subset of 7 possible linear 7 note arrangements.
It is all just a shifting grid. Once you can visualize it as such it becomes much easier to understand. To understand how keys work in relation to each other study the Circle of Fifths which may seem complex at first glance but is actually quite simple.
Start at C which has no sharps or flats then find the 5th note (which is G). G is now your new starting point in the CDEFGABC pattern. Sharp the 7th note (B) and you will have the key of G Major from which you can create all 7 modes of G Major. Then find the 5th note of G Major (which is D) and again sharp the 7th note. You have now created D major. Follow this pattern until every letter note is sharped. Then you have to switch over to using flat notes and the process kind of reverses and you remove flat notes to preserve the Major pattern until you return back to C.
You can do it in reverse starting from C and counting up to the 4th. We do not add the flats to the 7th though. We add them to the 4th. So find the fourth of C (which is F) then count up to the 4th (which is B). Flat the B. Now you have created the key of F Major. I refer to this as the Circle of Fourths and have seen it called that elsewhere as well but not very often.
When you do this you will notice that there are three keys in the middle that can be interpreted as either sharp or flat. They are:
C# = Db
F# = Gb
Cb = B
Usually you would use the sharp version to write in these keys but not always. Also in certain cases you will need to sharp a letter note even though the note above it is only a half step away (eg: E# = F in the key of F# Major). This is done to preserve the letter order because in diatonic scales you never use a letter note twice. You sharp or flat the letter names to create your pattern.
When writing the key sig onto the staff you write the sharps and flats in the order they appear within the circle of fifths or the circle of fourths. This means you start at C and add one sharp to the staff for each consecutive step on the circle of fifths and for the flat keys you start from C and add one flat to the key sig follow the circle of fourths.